For example, a problem is considered, in which a design parameter space is searched to obtain coordinates of a point that represents inferiority (hereinafter, referred to NG) and is nearest to the design center. For instance, as schematically depicted in FIG. 1, in the design parameter space mapped by the design parameters X1 and X2, the search starts from the design center that is set at the origin. In the search, an indicator representing goodness or badness of the design is prepared, and values of the indicator are calculated by the simulation. More specifically, the search was carried out by a method such as steepest descent method using the change of the indicator value when changing the values of the design parameters. In FIG. 1, the indicator values and their contour lines are schematically illustrated, and a portion whose indicator value is equal to or less than “0” corresponds to an NG area. As illustrated by an arrow, the search is carried out along a route whose inclination of the indicator value is greatest, and when the search reaches an NG point that is nearest to the design center (point represented by a circle), the search is completed.
However, there is a case where the indicator representing the goodness or badness of the design is not calculated as a continuous numerical value but is obtained only as success (OK) or failure (NG). For example, there is a case where only a judgment indicator exists such a judgment indicator representing data can be written or cannot be written to a Statistic Random Access Memory (SRAM) or judgment indicator representing a robot can stand up or cannot stand up. In such a case, when the number of design parameters is lesser, or when the search range is narrow, it is possible to identify a boundary between an area in which OK (e.g. judgment indicator=1) is determined and an area in which NG (e.g. judgment indicator=0) is determined, by searching thoroughly, as schematically illustrated in FIG. 2. However, when the number of design parameters is greater and the search range is broader, it is difficult to obtain the coordinates of the NG point that is nearest to the design center, by using such a method.
Then, it is considered that a search indicator to search the design parameter space is introduced in addition to the judgment indicator. The search indicator represents goodness or badness of the design at an arbitrary point in the design parameter space, and according to this search indicator, it is possible to determine the relative goodness or badness of the designs at two points. Therefore, it is also possible to carry out the search by using the steepest descent method or the like using this search indicator. However, the boundary between OK and NG by the search indicator and the boundary between OK and NG by the judgment indicator are not always identical. Then, the result of the search by the search indicator may not correspond to an NG point that is nearest to the design center. Furthermore, there is a case where only a local optimal solution can be obtained by the search using the steepest descent method or the like using the search indicator.
Incidentally, a technique exists to surely obtain trade-off information which exists between optimality and robustness by increasing the efficiency of time and labor to obtain a robust optimum solution, with which a designer is satisfied. Specifically, when an average value and a standard deviation of an inputted objective function are set as plural new independent multi-objective functions and also plural design candidates are generated based on the inputted initial values, a dominance indicator, which represents an evaluation result of the robust optimum solution, is calculated using an average and a standard deviation of sample points generated in the vicinity of each of design candidates, and the new design candidates are repetitively generated by replacing existing design candidates, while prioritizing the design candidate having a good dominance indicator. Therefore, it becomes possible to calculate plural robust optimum solutions by one optimization calculation, and to simply and efficiently find perspective of the trade-off information between the optimality and robustness of the objective functions by remarkably shortening calculation time required for calculating all the optimum solutions. However, the application of this method to the steepest descent method is not considered. In addition, because the dominance indicator is calculated for each design candidate, extra calculation time is required.